The practicing instrumentation engineer's guide to the DFT - Part 1: Understand DFT and FFT implementations

"When analyzing signal spectra in practice, we're normally interested in the relative magnitudes rather than absolute magnitudes of the individual DFT outputs, so scaling factors aren't usually important to us."

1. Understand the DFT and FFT Implementations available
2. Make waveforms and preform DFT's on real signals and calibrate the DFT output
3. Understand Window functions and their sources of error on our calibration
4. Look at the proper way to average DFT's to reduce variance
5. Discuss practical display techniques on limited resolution screens

1. Right now we live in a .NET world for the Windows based PC, so the experiments will be in Microsoft's free C# .NET Express version [1]. C# is a easily readable language so even if you don't use C# you will be able to understand the code and port it to your language of choice.
2. We will use a GNU DFT implementation and I choose ALGLIB [2] as it is easy to understand, easy to implement, has a version fully written in Managed C#, and others. There are many other DFT implementations available [3] and all of them are applicable to the discussion that follows by usually just changing a few lines of code.
3. For visualization we will be using the free .NET charting software ZedGraph available on Source Forge [4] which happens to plug in directly with the .NET framework and is quite easy to use.
4. All of the C# demonstration code is available as a free download that has working examples of every concept presented in this article [5].